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CAT 2019 Slot 1 — QA Question 28

Simple InterestEasy

Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?

Answer & solution

Correct answer: 7250

  • A

    7000

  • 7250

  • C

    6350

  • D

    6000

Solution

Easy

Interest ∝\propto (principal ×\times rate). Write principals as 3x,4x,5x3x,4x,5x and rates as 6r,5r,4r6r,5r,4r; each person's interest is the product. Use the "Bina exceeds Amala by 250" condition to pin down xrxr, then sum.

Principals 3x:4x:5x3x:4x:5x; rates 6r:5r:4r6r:5r:4r. Interest == principal ×\times rate.

1

Interest of each. Multiply principal by rate.

Amala=3x⋅6r=18xrBina=4x⋅5r=20xrGouri=5x⋅4r=20xr\begin{aligned} &\text{Amala}=3x\cdot 6r=18xr\\ &\text{Bina}=4x\cdot 5r=20xr\\ &\text{Gouri}=5x\cdot 4r=20xr \end{aligned}
2

Apply the given difference. Bina −- Amala =250=250.

20xr−18xr=250(from step 1)⇒ 2xr=250 ⇒ xr=125\begin{aligned} &20xr-18xr=250\quad\text{(from step 1)}\\ &\Rightarrow\ 2xr=250\ \Rightarrow\ xr=125 \end{aligned}
3

Total interest. Add the three amounts.

18xr+20xr+20xr=58xr⇒ =58×125(from step 2)⇒ =7250\begin{aligned} &18xr+20xr+20xr=58xr\\ &\Rightarrow\ =58\times 125\quad\text{(from step 2)}\\ &\Rightarrow\ =7250 \end{aligned}
Total interest=Rs 7250\text{Total interest}=\text{Rs }7250

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CAT 2019 Slot 1 QA Q28: Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest — Solution | TheCATExam