Simple Interest

Sponsor Area

Question
SSCCGLENQA12043120

A man invested 1 third of his capital at 7%, 1 fourth at 8% and the remaining at 10% rate of simple interest. If his annual income from interests is Rs. 561, the capital invested was

  • Rs. 6000

  • Rs. 5600

  • Rs. 6600

  • Rs. 7200

Solution

C.

Rs. 6600

Let the total capital invested be Rs. x then,
fraction numerator begin display style straight x over 3 cross times 7 end style over denominator 100 end fraction space plus space fraction numerator begin display style straight x over 4 space cross times space 8 end style over denominator 100 end fraction space plus space fraction numerator begin display style fraction numerator 5 straight x over denominator 12 end fraction cross times 10 end style over denominator 100 end fraction space equals space 561
                             open square brackets straight S. straight I. space equals space fraction numerator straight P. straight R. straight T over denominator 100 end fraction close square brackets
rightwards double arrow space space space space fraction numerator 7 straight x over denominator 300 end fraction space plus space fraction numerator 2 straight x over denominator 100 end fraction space plus space fraction numerator 25 straight x over denominator 600 end fraction space equals space 561
rightwards double arrow space space space fraction numerator 14 straight x space plus space 12 straight x space plus space 25 straight x over denominator 600 end fraction space equals space 561
rightwards double arrow space space fraction numerator 51 straight x over denominator 600 end fraction space equals space 561
rightwards double arrow space space space straight x space equals space fraction numerator 561 space cross times space 600 over denominator 51 end fraction space equals space Rs. space 6600

Sponsor Area

Question
SSCCGLENQA12042930

A person has left an amount of ₹ 1,20,000 to be divided between his two sons aged 14 years and 12 years such that they get equal amounts when each attains 18 years of age. If the amount gets a simple interest of 5% per annum, the younger son's share at present is

  • ₹ 48,800

  • ₹ 57,600

  • ₹ 62,400

  • ₹ 84,400

Solution

B.

₹ 57,600

Let the younger son's share be Rs x.
∴  Elder son's share  = Rs. (120000 - x)
Now, According to the question
rightwards double arrow space space space space space straight x plus fraction numerator straight x cross times 5 cross times 6 over denominator 100 end fraction space equals space left parenthesis 120000 minus straight x right parenthesis space plus space fraction numerator left parenthesis 120000 minus straight x right parenthesis space cross times space 4 space cross times space 5 over denominator 100 end fraction
rightwards double arrow space space 20 straight x space plus space 6 straight x space equals space 20 space cross times space 120000 space minus space 20 straight x space plus space 480000 space minus space 4 straight x
rightwards double arrow space space space space space space 50 straight x space equals space 2400000 space plus space 480000
rightwards double arrow space space space space space 50 straight x space equals space 2880000
rightwards double arrow space space space space straight x space equals space 2880000 over 50 space equals space Rs. space 57600

Question
SSCCGLENQA12042693

A shopkeeper sold an item at 10% loss after giving a discount equal to half of the marked price. Then the cost of price is

  • 1 over 9 th space of space marked space price
  • 4 over 9 th space of space markd space price
  • 5 over 9 th space of space marked space price
  • 7 over 9 th space of space marked space price

Solution

C.

5 over 9 th space of space marked space price

Let the marked price be Rs. 100
Discount =  50% on 100 = Rs. 50
S.P.(Selling Price) = Rs. (100 - 50) = Rs 50
Now,
straight C. straight P. space equals space open parentheses fraction numerator 50 space cross times space 100 over denominator left parenthesis 100 minus 10 right parenthesis end fraction close parentheses space equals space 50 over 90 space cross times space 100 space equals space 5 over 9 space of space marked space price

Question
SSCCGLENQA12042481

A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352. The sum lent at 8% is

  • Rs. 2900

  • Rs. 2200

  • Rs. 2400

  • Rs. 3100

Solution

C.

Rs. 2400

By Shortcut Method:
Required solution = 8% on 4000 = Rs.320
                          = 10% on 4000 = Rs.400
                    Now, Rs (352 - 320) = Rs 32    ...(i)
                            Rs (400 - 352) = Rs. 48   ...(ii)
Take the opposite ratios from equation (i) and (ii),
i.e. Rs .48 : Rs 32
           3 : 2
Thus, Sum lent at 8% is 
open parentheses 3 over 5 cross times 4000 space close parentheses space equals space Rs. space 2400
 

Question
SSCCGLENQA12043201

A sum of Rs. 7,930 is divided into three parts and given on loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then A received a loan of

  • Rs. 3,050

  • Rs. 2,760

  • Rs. 2,750

  • Rs. 2,800

Solution

B.

Rs. 2,760

(100 + 5 x 2)% of A = (100 + 5 x 3)% of B = (100 + 5 x 4)% of C
110% of A = 115% of B = 120% of C = k(Let)
therefore space space straight a space colon space straight b space colon space straight c space equals space 1 over 110 space colon space 1 over 115 space colon space 1 over 120
space equals space 1 over 22 space colon space 1 over 23 space colon space 1 over 24 space equals space 23 space cross times space 24 space colon space 22 space cross times space 24 space colon space 22 space cross times space 23
∴  Loan received by A
  equals space fraction numerator 23 space cross times space 24 over denominator 1586 end fraction cross times 7930 space equals space ₹ 2760

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